mars.tensor.fft.ifftn¶

mars.tensor.fft.
ifftn
(a, s=None, axes=None, norm=None)[source]¶ Compute the Ndimensional inverse discrete Fourier Transform.
This function computes the inverse of the Ndimensional discrete Fourier Transform over any number of axes in an Mdimensional tensor by means of the Fast Fourier Transform (FFT). In other words,
ifftn(fftn(a)) == a
to within numerical accuracy. For a description of the definitions and conventions used, see mt.fft.The input, analogously to ifft, should be ordered in the same way as is returned by fftn, i.e. it should have the term for zero frequency in all axes in the loworder corner, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency.
 Parameters
a (array_like) – Input tensor, can be complex.
s (sequence of ints, optional) – Shape (length of each transformed axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). This corresponds ton
forifft(x, n)
. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. if s is not given, the shape of the input along the axes specified by axes is used. See notes for issue on ifft zero padding.axes (sequence of ints, optional) – Axes over which to compute the IFFT. If not given, the last
len(s)
axes are used, or all axes if s is also not specified. Repeated indices in axes means that the inverse transform over that axis is performed multiple times.norm ({None, "ortho"}, optional) – Normalization mode (see mt.fft). Default is None.
 Returns
out – The truncated or zeropadded input, transformed along the axes indicated by axes, or by a combination of s or a, as explained in the parameters section above.
 Return type
complex Tensor
 Raises
ValueError – If s and axes have different length.
IndexError – If an element of axes is larger than than the number of axes of a.
See also
mt.fft
Overall view of discrete Fourier transforms, with definitions and conventions used.
fftn
The forward ndimensional FFT, of which ifftn is the inverse.
ifft
The onedimensional inverse FFT.
ifft2
The twodimensional inverse FFT.
ifftshift
Undoes fftshift, shifts zerofrequency terms to beginning of tensor.
Notes
See mt.fft for definitions and conventions used.
Zeropadding, analogously with ifft, is performed by appending zeros to the input along the specified dimension. Although this is the common approach, it might lead to surprising results. If another form of zero padding is desired, it must be performed before ifftn is called.
Examples
>>> import mars.tensor as mt
>>> a = mt.eye(4) >>> mt.fft.ifftn(mt.fft.fftn(a, axes=(0,)), axes=(1,)).execute() array([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])
Create and plot an image with bandlimited frequency content:
>>> import matplotlib.pyplot as plt >>> n = mt.zeros((200,200), dtype=complex) >>> n[60:80, 20:40] = mt.exp(1j*mt.random.uniform(0, 2*mt.pi, (20, 20))) >>> im = mt.fft.ifftn(n).real >>> plt.imshow(im.execute()) <matplotlib.image.AxesImage object at 0x...> >>> plt.show()